## Friday, October 1, 2021

### Derivative value

Some things have derivative value. One kind of derivation is from whole to parts: a stone can have a special value by virtue of being a part of something of great significance, say a temple. Another kind of derivation is from parts to whole: a golden statue has a value deriving from the value of its atoms. Yet another kind is from friend to friend: if I do good directly to a friend of yours, I benefit you as well.

The distinction between derivative and original value is orthogonal to that between instrumental and non-instrumental value, and probably also to that between intrinsic and extrinsic value.

It is easy to create puzzles with derivative value, because derivative value is not simply additive and double counting must be avoided. Imagine a golden statue made by someone with minimal artistic skill. The maker of that statue then produced something literally worth its weight in gold, and yet they added almost no value to the world, because almost all of the value of the poorly made statue is derivative. Melting down a golder statue worth exactly its weight in gold does no harm to the world! Similarly, dissolving a ten-member committee need be no more harmful than dissolving a five-member one.

If two people are drowning, one friendless and one with ten friends, perhaps there is additional reason to save the one with ten friends, though the point is not clear. But if there is additional reason, it does not scale linearly with the number of friends. If someone had a thousand of friends, that needn’t create much more a reason to save them than if they had a hundred, I suspect.

It is tempting to initially think of derivative value as a faint shadow of original value. Sometimes this is true: the death of Alice considered as a derivative harm to her distant friends is a mere shadow of the badness of that death considered as a harm to Alice. But sometimes it’s not true: the death of Alice considered as a derivative harm to her closest friends approaches the original badness of that death considered as a harm to her. And the inartistic golden statue’s derivative value is not a whit less than the original value of its gold components.

Can we at least say that derivative value is always at most equal to the original value? Maybe, but even that is not completely clear. That Alice is loved by God makes it be the case that a harm to Alice is a harm to God. But it could be that the derivative badness to God gives us reasons to protect Alice that are stronger than those coming from the original badness to Alice, and the derivative badness here might exceed the original badness. (Recall here Anselm’s idea that sin is infinitely bad, because it offends the infinite God.) Perhaps, though, cases of love do not give rise to purely derivative value, because the derivative value is created by an interaction between the original value of the beloved and the original value of the lover. On the other hand, insofar as the inartistic golden statue’s value is purely derivative, it cannot exceed the original value of the parts.

The non-additiveness of derivative value throws a wrench in simple consequentialist systems on which we maximize the total value of everything. Perhaps, though, it is possible to talk about overall value, which is not additive in nature, so this need not be a knock-down argument against consequentialism. But it definitely seems to complicate things.

Note that similar phenomena occur for other properties than value. When one takes ten pounds of gold and makes a statue of it, one may create a ten pound object (assuming for the sake of argument that statues really exist), but one doesn’t add ten pounds to reality. We need to avoid double-counting in the case of derivative mass just as much as for derivative value.

shakil khan said...

Hi Alex
Its a unrelated comment but I hope you will respond.

Its about the cosmological argument you developed with Richard M. Gale using WPSR . Recently I have come across a challenge to your argument. the argument in a nutshell goes like this, because the proposition q explains p is contingent and is not part of BCCF it follows that in a possible world W2 p is true but q doesn't explain p.so without q or its negation being part of BCCF you cannot individuate the possible worlds.Hence your unjustified in saying W1 is the actual world from p being true in that world since p is true in W2 as well. And thus your argument fails.